Given $ m \angle RPS = 7x - 124$, $ m \angle QPR = 4x - 44$, and $ m \angle QPS = 52$, find $m\angle RPS$. $P$ $Q$ $S$ $R$
Explanation: From the diagram, we see that together ${\angle QPR}$ and ${\angle RPS}$ form ${\angle QPS}$ , so $ {m\angle QPR} + {m\angle RPS} = {m\angle QPS}$ Substitute in the expressions that were given for each measure: $ {4x - 44} + {7x - 124} = {52}$ Combine like terms: $ 11x - 168 = 52$ Add $168$ to both sides: $ 11x = 220$ Divide both sides by $11$ to find $x$ $ x = 20$ Substitute $20$ for $x$ in the expression that was given for $m\angle RPS$ $ m\angle RPS = 7({20}) - 124$ Simplify: $ {m\angle RPS = 140 - 124}$ So ${m\angle RPS = 16}$.